System and method for gyro rate computation for a Coriolis Vibrating Gyroscope

ABSTRACT

In accordance with one or more aspects of the present disclosure, a method including supplying a first voltage input to a Coriolis vibratory gyroscope at a first bias voltage; supplying a second voltage input to the Coriolis vibratory gyroscope at a second bias voltage, the second bias voltage being different than the first bias voltage; detecting a difference in responses of the Coriolis vibratory gyroscope due to the first bias voltage and the second bias voltage; and determining a gyro rate of the Coriolis vibratory gyroscope as a function of the difference in responses and a correction term.

FIELD

The exemplary embodiments generally relate to calibration of CoriolisVibratory Gyroscopes, and in particular, calibration of CoriolisVibratory Gyroscopes with dual bias voltage measurements.

BRIEF DESCRIPTION OF RELATED DEVELOPMENTS

Gyroscopes have long been in use in many industries, including theaerospace, maritime and defense industries for determining theorientation of a device or machine. In recent years, gyroscopes alsofound applications in consumer electronics—notably smartphones andglobal positioning system receivers. One classification of gyroscopescommonly in use today is Coriolis Vibratory Gyroscopes (also known asCoriolis resonating gyroscopes or vibrating structure gyroscopes).Coriolis Vibratory Gyroscopes, unlike their spinning mechanicalgyroscope counterparts, are solid state and operate by using a vibratingstructure to determine a rate of rotation of the gyroscope. Thevibrating structure of Coriolis Vibratory Gyroscopes continues tovibrate in the same plane, even as the orientation of the CoriolisVibratory Gyroscope is changed due to the force exerted on the CoriolisVibratory Gyroscope support by the Coriolis effect as the orientation ofthe Coriolis Vibratory Gyroscope is changed. By measuring the forceexerted on the support due to the Coriolis effect, the rate of rotationof the Coriolis Vibratory Gyroscope can be determined, and in turn, theorientation of the Coriolis Vibratory Gyroscope can also be determined.

However, Coriolis Vibratory Gyroscopes can experience drift errors wherethe instrument scale factor has been corrupted and is no longer capableof giving consistent output. Conventionally, Coriolis VibratoryGyroscopes experiencing drift errors can be calibrated or re-calibratedwith an external reference to correct for the drift and the corruptedscale factors. However, in many situations, no external references areavailable to recalibrate after the deployment of the Coriolis VibratoryGyroscope. This is especially true, for example, in missile systems,spacecraft or in other devices or machines that cannot be easilyrecalled for recalibration once deployed. Conventional calibrationtechniques are simply not sufficient for these applications.

Historically, for mechanical spinning mass gyroscopes, an alternativemethod of calibration called “wheel speed modulation” was the subject ofexperiments. “Wheel speed modulation” was successfully demonstrated toprovide azimuth determination in the absence of case rotation andprovided ramp bounding to minimize drift errors by several magnitudes.The operation of “wheel speed modulation” is based on different torquesbeing applied to the spinning mass of a mechanical gyroscope produced bymechanisms which are unrelated to the magnitude of the gyroscope angularmomentum. By modulating the speed and the momentum of the spinninggyroscope mass, a bias can be determined based on the output of thegyroscope which can be employed to determine the drift of the mechanicalgyroscope. When two different torque measurements are solvedsimultaneously, a bias variation can be determined which is constant.The constant bias variation allows for field-derived values of angularrate input.

However, despite the success of “wheel speed modulation” in thelaboratory, this technique may not be practical. In order to accommodatethe modulation of the speed of the spinning mass in mechanicalgyroscopes, the “wheel speed modulation” method is relatively slow,because it takes time for the differential torque applied to thespinning mass of a mechanical gyroscope to result in the desired wheelspeed modulation. There may also be issues with repeatability inmodulating the speed of the spinning mass of the mechanical gyroscope,which makes “wheel speed modulation” impractical for widespreaddeployment.

SUMMARY

In accordance with one or more aspects of the present disclosure, amethod including supplying a first voltage input to a Coriolis vibratorygyroscope at a first bias voltage, supplying a second voltage input tothe Coriolis vibratory gyroscope at a second bias voltage, the secondbias voltage being different than the first bias voltage, detecting adifference in responses of the Coriolis vibratory gyroscope due to thefirst bias voltage and the second bias voltage, and determining a gyrorate of the Coriolis vibratory gyroscope as a function of the differencein responses and a correction term.

In accordance with one or more aspects of the present disclosure, asystem including a Coriolis vibratory gyroscope, a voltage input supplyconfigured to supply a first voltage input to the Coriolis vibratorygyroscope at a first bias voltage, and supply a second voltage input tothe Coriolis vibratory gyroscope at a second bias voltage, the secondbias voltage being different than the first bias voltage, and acontroller configured to detect a difference in responses of theCoriolis vibratory gyroscope due to the first bias voltage and thesecond bias voltage, and determine a gyro rate of the Coriolis vibratorygyroscope as a function of the difference in responses and a correctionterm.

In accordance with one or more aspects of the present disclosure, amethod including determining scale factors for a first voltage input ata first bias voltage and a second voltage input at a second bias voltagefor a Coriolis vibratory gyroscope, providing the first voltage input tothe Coriolis vibratory gyroscope at the first bias voltage and detectinga first response of the Coriolis vibratory gyroscope, providing thesecond voltage input to the Coriolis vibratory gyroscope at the secondbias voltage and detecting a second response of the Coriolis vibratorygyroscope, and using a difference of the first response and the secondresponse, the scale factors for the first voltage input and the secondvoltage input, and a gyro rate of the Coriolis vibratory gyroscope todetermine a correction term representing a function of a difference ofthe time-dependent instrument bias in the first response and the secondresponse.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus described examples of the disclosure in general terms,reference will now be made to the accompanying drawings, which are notnecessarily drawn to scale, and wherein like reference charactersdesignate the same or similar parts throughout the several views, andwherein:

FIG. 1 is a block diagram of a Coriolis Vibratory Gyroscope system inaccordance with one or more aspects of the present disclosure;

FIG. 2 is an exemplary flow diagram for computing a gyro rate of theCoriolis Vibratory Gyroscope in accordance with one or more aspects ofthe present disclosure;

FIG. 3 is an exemplary flow diagram for computing a correction term ofthe Coriolis Vibratory Gyroscope in accordance with one or more aspectsof the present disclosure; and

FIG. 4 is a schematic illustration of an aerospace vehicle in accordancewith one or more aspects of the present disclosure.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toprovide a thorough understanding of the disclosed concepts, which may bepracticed without some or all of these particulars. In other instances,details of known devices and/or processes have been omitted to avoidunnecessarily obscuring the disclosure. While some concepts will bedescribed in conjunction with specific examples, it will be understoodthat these examples are not intended to be limiting.

Reference herein to “one example” or “one aspect” means that one or morefeature, structure, or characteristic described in connection with theexample or aspect is included in at least one implementation. The phrase“one example” or “one aspect” in various places in the specification mayor may not be referring to the same example or aspect.

Unless otherwise indicated, the terms “first,” “second.” “third,” etc.are used herein merely as labels, and are not intended to imposeordinal, positional, or hierarchical requirements on the items to whichthese terms refer. Moreover, reference to, e.g., a “second” item doesnot require or preclude the existence of, e.g., a “first” orlower-numbered item, and/or, e.g., a “third” or higher-numbered item.

Referring to FIG. 1, a Coriolis Vibratory Gyroscope (CVG) system 100 isillustrated. Aspects of the present disclosure provide a system fordetermining a rate of rotation for a Coriolis Vibratory Gyroscope, wherethe scale factor(s) for the CVG have become corrupted or wheregyroscopic drift has occurred, which addresses the deficiencies ofconventional gyroscope calibration methods noted above. In one aspect,the CVG system 100 includes a Coriolis Vibratory Gyroscope 101 coupledto a CVG support 105, a voltage input supply 102, a voltage detector103, and a controller 104. In one aspect, CVG 101 is a hemisphericalresonator gyroscope. However, in other aspects, the CVG 101 can includetuning fork gyroscopes, cylindrical vibratory gyroscopes,micro-electromechanical (MEM) gyroscopes, piezoelectric gyroscopes, orany suitable Coriolis Vibratory Gyroscope or solid-state gyroscope whichoperates on the principle of the Coriolis effect.

In one aspect, the voltage input supply 102 is connected to the CVG 101and is configured to supply a first voltage to the CVG 101 at a firstbias voltage P₀ and supply a second voltage input to the CVG 101 at asecond bias voltage P₀′, where the second bias voltage P₀′ is differentthan the first bias voltage P₀. In one aspect, the first bias voltage P₀and second bias voltage P₀′ supplied by the voltage input supply 102each are associated with a different, respective predetermined scalefactor S₀, S₀′ of the CVG 101. In one aspect, for example P₀′=P₀/S₀′.

In one aspect, the CVG 101 is configured to output a first response V₀(in the form of a voltage output) in response to the first bias voltageP₀ and a second response V₀′ (in the form of a different voltage output)in response to the second bias voltage P₀′. In one aspect, each of thefirst response V₀ and second response V₀′ output by the CVG 101 aredetected by the voltage detector 103, which is in communication with thecontroller 104. In one aspect, the voltage detector 103 is a standalonesensor. However, in other aspects, the voltage detector 103 is a part ofthe controller 104 (as shown in the dashed lines in FIG. 1). In oneaspect, the controller 104 (in conjunction with the voltage detector103) is configured to detect and determine a difference in the first andsecond responses V₀, V₀′ of the CVG 101 due to the first bias voltage P₀and the second bias voltage P₀′ respectively. In one aspect, thedifference in the first and second responses V₀, V₀′ of the CVG 101 dueto the first and second bias voltages P₀, P₀′, as determined by thecontroller 104 (and the voltage detector 103), is represented as achange in voltage output of the CVG 101 from the first response V₀ atthe first bias voltage P₀ to the second response V₀′ at the second biasvoltage P₀′. This change in voltage output of the CVG 101 provides afirst scale factor S₀ corresponding to the first response V₀ and asecond scale factor S₀′ corresponding to the second response V₀′ for acommon voltage input to the CVG 101. In one aspect, the difference inthe first and second responses V₀, V₀′ of the CVG 101 to the first biasvoltage P₀ and second bias voltage P₀′ is constant.

In one aspect, the controller 104 is also configured to determine a gyrorate Ω of the CVG 101 as a function of the difference in the first andsecond responses V₀, V₀′ as well as a correction term C. The gyro rate Ωof the CVG 101 is a rate of rotation of the CVG 101 and is independentof the scale factors S₀, S₀′ of the CVG 101 at the first bias voltage P₀and second bias voltage P₀′. The correction term C is a predeterminedconstant value based on the first and second responses V₀ and V₀′ andinitial input rate of the CVG 101 at the first bias voltage P₀ and thesecond bias voltage P₀′.

In one aspect, during the operation of the CVG 101, a bias of the CVG101 (e.g., a non-zero gyro rate Ω when an input inertial rate is zero)and the first and second scale factors S₀, S₀′ may drift due to a numberof factors, including extended use of the CVG 101, temperature orenvironmental changes or other factors. In one aspect, the controller104 is configured to determine the gyro rate Ω and the correction term Cof the CVG 101 independently of the drift imparted on the first andsecond scale factors S₀, S₀′ and the bias of the CVG 101. In one aspect,the controller 104 is configured to determine the gyro rate and thecorrection term C by a model to be derived below.

In one aspect, consider the IEEE standard 1431-2004 model for the closedloop scale factor for Coriolis Vibratory Gyroscopes, represented as:SV=[ω+D][1+10⁻⁶ε_(k)]⁻¹  EQ1:

Where S is a scale factor (e.g., scale factors S₀ and S₀′) for a voltageoutput, V is the voltage output (e.g., the first and second responsesV₀, V₀′) in volts, D is the drift rate (°/h), ε_(k) is the scale factorerror (ppm) and ω is the inertial input (°/h).

In one aspect. EQ1 can be generalized as:V=Ω+Df  EQ2:

Where Df represents the instrument bias of the CVG 101 at, for example,a predetermined voltage output V in response to, for example, apredetermined bias voltage P. In one aspect, EQ2 is analogous to themodel for mechanical gyroscopes:T=H*Ω+Df  EQ3:

where T represents torque.

In one aspect, when the first and second bias voltages P₀, P₀′ areapplied to the CVG 101, the resulting first and second responses V₀, V₀′of the CVG 101 to the first and second bias voltages P₀, P₀′ can berepresented as two different equations EQ4 and EQ5 which are based onEQ2, described above.V ₀ =Ω+Df  EQ4:V ₀ ′=Ω+D{acute over (f)}  EQ5:

Where Df represents the instrument bias of the CVG 101 at the firstresponse V₀ in response to the first bias voltage P₀ and D{acute over(f)} represents the instrument bias at the second response V₀′ inresponse to the second bias voltage P₀′ and where the correction term Ccan be defined as:Df−Df=C  EQ6:

The correction term C, as described in EQ6, is a constant that is fieldor factory calibrated. When EQ4 and EQ5 are solved together for the gyrorate Ω, given EQ6, equations EQ7 and EQ8 are derived, which enables thecontroller 104 to determine the gyro rate Ω for the CVG 101:Ω=(V ₀ −V ₀ ′−C)/2  EQ7:

Where (V₀−V₀′−C) is divided by 2 for half scale factor change.

The more general form of EQ7 can be expressed as EQ8:

$\begin{matrix}{\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}} & {EQ8}\end{matrix}$

where the change in scale factor is a constant and where S₀ is the firstscale factor and S₀′ is the second scale factor, V₀ is the firstresponse at the first bias voltage P₀, V₀′ is the second response at thesecond bias voltage P₀′, and C is the correction term. In one aspect,the difference between the first and second responses V₀, V₀′ of the CVG101 to the first bias voltage and second bias voltage P₀, P₀′ isconstant. In one aspect, by applying EQ8 given the first and secondresponses V₀, V₀′ of the CVG 101 to the first and second bias voltagesP₀, P₀′ and given the first and second scale factors S₀, S₀′, thecontroller 104 can determine the gyro rate Ω of the CVG 101independently of calibration of the first scale factor S₀ and thecalibration of the second scale factor S₀′ where the time dependentinstrument bias of the CVG 101 caused the first scale factor S₀ and thesecond scale factor S₀′ to shift equally.

In one aspect, the following example is provided for exemplary purposesonly to show that the gyro rate Ω can be obtained independently of thecalibration of the first scale factor S₀ and the calibration of thesecond scale factor S₀′ and the time dependent instrument bias of theCVG 101. All numbers and figures presented below are for exemplarypurposes only.

Assuming that there is a first and a second bias voltage P₀ and P₀′given an input gyro rate Ω, where

${P_{0} = \frac{\Omega}{S_{0}}},\mspace{14mu}{P_{0}^{\prime} = \frac{\Omega}{S_{0}^{\prime}}},$and the first and second bias voltage P₀ and P₀′ respectively have afirst scale factor S₀ of, e.g.,

$1\frac{v}{{rad}/\sec}$and a second scale factor S₀′ of, e.g.,

${0.4\frac{v}{{rad}/\sec}},$where the input gyro rate Ω is, for example,

$160\frac{rad}{\sec}$(which is the anticipated pulse rate output or output gyro rate Ω′ ofthe CVG 101), P₀ is, for example, 160/1 and P₀′ is, for example,160/0.4. As such, P₀*S₀=160 and P₀′*S₀′=160. If the first bias voltageP₀ and second bias voltage P₀′ are multiplied with their respectivescale factors S₀, S₀′, the anticipated gyro rate Ω is

$160\frac{rad}{\sec}$for both.P ₀ *S ₀=(160/1)*1=160P ₀ ′*S ₀′=(160/0.4)*0.4=160

If time dependent instrument bias B₀ and B₀′ are introduced into thecalculation, then the measured voltage output M₁, M₂ corresponding tothe first response V₀ and second response V₀′ respectively will nolonger equal 160.

Given an exemplary first instrument bias

$B_{0} = {5\frac{rad}{\sec}}$and an exemplary second instrument bias

$B_{0}^{\prime} = {3\frac{rad}{\sec}\text{:}}$M ₁=(P ₀ +B ₀)*S ₀=165M ₂=(P ₀ ′+B ₀′)*S ₀′=161.2

Knowing EQ4 and EQ5 and given EQ6, shown above, the first and secondvoltage responses V₀ and V₀′ can be represented as:V ₀ =P ₀ +B ₀=165V ₀ ′=P ₀ ′+B ₀′=403

By applying the first and second voltage responses V₀, V₀′ to EQ6, thecorrection term C can be derived.C=B ₀ −B ₀′=2

By applying the exemplary values of the first and second voltageresponses V₀, V₀′ and the scale factors S₀, S₀′ and the correction term,the output gyro rate Ω′ can be determined by the controller 104:

$\Omega^{\prime} = {\frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}\mspace{14mu}{Or}\text{:}}$$\Omega^{\prime} = {\frac{\left( {165 - 403 - 2} \right)}{\frac{1}{1} - \frac{1}{.4}} = {160\frac{rad}{\sec}}}$

Thus, the output gyro rate Ω′ is the same as the input gyro rate Ω, andcan be determined from EQ8 independently of the calibration of the firstscale factor S₀, the calibration of the second scale factor S₀′ and thetime dependent instrument bias (e.g. B₀, B₀′) of the CVG 101.

In another aspect, another example is provided for exemplary purposesbelow. All numbers and figures presented below are for exemplarypurposes only.

Assuming that there is a first and a second bias voltage P₀ and P₀′given an input gyro rate Ω of

${100\frac{rad}{\sec}},$where

${P_{0} = \frac{\Omega}{S_{0}}},{P_{0}^{\prime} = \frac{\Omega}{S_{0 \wr}^{\prime}}},$and the first and second bias voltage P₀ and P₀′ respectively have afirst scale factor S₀ of, e.g.,

$1.5\;\frac{v}{{rad}/\sec}$and a second scale factor S₀′ of, e.g.,

${3\frac{v}{{rad}/\sec}},$P₀ is, for example, 100/1.5 (or about 66.667) and P₀′ is, for example,100/3 (or about 33.333). If the first bias voltage P₀ and second biasvoltage P₀′ are multiplied with their respective scale factors S₀, S₀′as described above, the anticipated gyro rate Ω is

$100\;\frac{rad}{\sec}$for both.

When an exemplary first and second instrument bias are provided, such asa bias

$B_{0}\mspace{14mu}{of}\mspace{14mu}{.9}\frac{rad}{\sec}$for the first bias voltage P₀ and a bias B₀′ for the second bias voltageP₀′ are introduced, we can calculate the first and second voltageresponses V₀ and V₀′ as:V ₀ =P ₀ +B ₀=66.667+0.9=67.567V ₀ ′=P ₀ ′+B ₀′=33.333+1.1=34.433

By applying the first and second voltage responses V₀, V₀′ to EQ6, thecorrection term C can be derived.C=B0−B0′=0.9−1.1=−0.2

By applying the exemplary values of the first and second voltageresponses V₀, V₀′, the scale factors S₀, S₀′ and the correction term, anoutput gyro rate Ω′ can be determined by the controller 104:

$\Omega^{\prime} = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$${{Or}:\Omega^{\prime}} = {\frac{\left( {67.567 - 34.433 + 0.2} \right)}{\frac{1}{1.5} - \frac{1}{3}} = {100\frac{rad}{\sec}}}$

Again, the output gyro rate Ω′ is the same as the input gyro rate Ω, andcan be determined from EQ8 independently of the calibration of the firstscale factor S₀, the calibration of the second scale factor S₀′ and thetime dependent instrument bias (e.g., B₀, B₀′) of the CVG 101.

Referring now to FIG. 2, a method for determining the gyro rate Ω isshown. At block 201, the first voltage input is applied to the CVG 101at the first bias voltage by the voltage input supply 102. At block 202,the second voltage input is applied to the CVG 101 at the second biasvoltage by the voltage input supply 102. As noted previously, the firstand second voltage inputs are different from each other.

At block 203, the controller 104 (and the voltage detector 103) isconfigured to detect a difference in the first and second responses V₀,V₀′ of the CVG 101 to the first bias voltage P₀ and the second biasvoltage P₀′. In one aspect, the difference in responses of the CVG 101is represented as a change in voltage output of the CVG 101 from a firstvoltage output (e.g. the first response V₀) at the first bias voltage P₀to a second voltage output (e.g. the second response V₀′) at the secondbias voltage P₀′, which provides a first scale factor S₀ correspondingto the first response V₀ and a second scale factor S₀′ corresponding tothe second response V₀′ for a common voltage input to the CVG 101. Inone aspect, the difference in responses of the CVG 101 to the first biasvoltage and second bias voltage is constant. At block 204, thecontroller is configured to determine the gyro rate Ω of the CVG 101 asa function of the difference in the first and second responses V₀, V₀′and the correction term C using EQ1 provided above. In one aspect, thefirst response V₀ by the CVG 101 in response to the first bias voltageP₀ and the second response V₀′ in response to the second bias voltageP₀′ and the correction term C represents a sum of the time dependentinstrument bias in response to the first response V₀ and the secondresponse V₀′. Further, in one aspect, the gyro rate Ω is determinedindependently of the scale factors of the CVG 101. In one aspect, thecontroller 104 further determines the gyro rate of the CVG 101 as afunction of the difference in the first and second responses V₀, V₀′ andthe correction term C, independent of calibration of the first scalefactor S₀ and the calibration of the second scale factor S₀′, where thetime dependent instrument bias causes the first scale factor S₀ and thesecond scale factor S₀′ to shift equally.

Referring now to FIG. 3, a method for determining the correction term Cis illustrated. At block 301, the controller 104 determines the scalefactors S₀, S₀′ for a first voltage input at a first bias voltage P₀ anda second voltage input at a second bias voltage P₀′ for a CVG 101. Inone aspect, this is known to the controller 104 or pre-computed. Atblock 302, the voltage input supply 102 provides the first voltage inputto the CVG 101 at the first bias voltage P₀. The controller 104 andvoltage detector 103 detects the first response V₀ of the CVG 101 inresponse to the first voltage input.

At block 303, the voltage input supply 102 provides the second voltageinput to the CVG 101 at the second bias voltage P₀′. The controller 104and voltage detector 103 detects the second response V₀′ of the CVG 101in response to the second voltage input. At block 304, the controlleruses a difference of the first response V₀ and the second response V₀′,the scale factors S₀, S₀′ calculated for the first voltage input and thesecond voltage input, the gyro rate Ω of the CVG 101 to determine thecorrection term C representing the function of a difference of a timedependent instrument bias in the first response and the second response.A model for computing the correction term C may be derived as follows.In one aspect, the controller 104 determines the correction term C basedon EQ1 determined above. EQ1 can be rewritten into EQ8, which expressesthe correction term C as:

$\begin{matrix}{C = {\left( {V_{0} - V_{0}^{\prime}} \right) - {\left( {\frac{1}{S_{0}} + \frac{1}{S_{0}^{\prime}}} \right)\Omega}}} & {{EQ}\mspace{14mu} 8}\end{matrix}$

The gyro rate Ω is determined by the controller 104 independent of thecalibration of the first scale factor S₀ and calibration of the secondscale factor S₀′ where the time dependent instrument bias causes thefirst scale factor S₀ and second scale factor S₀′ to shift equally.Because the gyro rate Ω is independent of the calibration of the firstscale factor and second scale factor S₀, S₀′, the drift of the CVG 101can be determined independently of the corrupted first scale factor andcorrupted second scale factor.

As shown in FIGS. 1 and 4, in one aspect, the CVG system 100 isincorporated into a vehicle 10 (described in greater detail below) forguiding the vehicle 10 along a predetermined path or trajectory oftravel. In one aspect, the CVG system 100 is part of a navigation system15 of the vehicle 10. Here, the vehicle 10 is configured to use thenavigation system 15 and the CVG system 100 to navigate the vehicle 10from a first location to a second location. While the vehicle 10 isrepresented as an aerospace vehicle for exemplary purposes, in otheraspects, the vehicle 10 may also be a maritime vehicle, an automotivevehicle, an amphibious vehicle or any other suitable vehicle. In yetother aspects, the vehicle 10 may also include consumer electronicsvehicles such as remote-controlled quadcopters or autonomous orsemi-autonomous vehicles such as self-driving and self-balancingvehicles. In one aspect, the navigation system 15 can be gyroscopic, butin other aspects, the navigation system 15 includes the CVG system 100as a component of a larger navigation system (for example, globalpositioning system navigation systems). In one aspect, the vehicle 10,as shown in FIG. 4, also includes an aerospace vehicle controller 401, apropulsion system 402, control surfaces 403 and a power supply 404 whichprovides power to, for example, the voltage input supply 102 of the CVGsystem 100. In one aspect, the controller 104 is part of a controllerfor the navigation system 15 or a part of the aerospace vehiclecontroller 401 for the vehicle 10. In yet other aspects, the controller104 is in communication with the controller for the navigation system 15or the aerospace vehicle controller 401 for the vehicle 10. In oneaspect, the navigation system 15 and the CVG system 100 is incommunication with the aerospace vehicle controller 401, which is, inturn, in communication with the propulsion system 402 and the controlsurfaces 403. In one aspect, the aerospace vehicle controller 401 isconfigured to use feedback from the navigation system 15 and the CVGsystem 100 to control the operation of the propulsion system 402 and thecontrol surfaces 403 so as to control the trajectory of the vehicle 10in flight. In other aspects, the aerospace vehicle controller 401 isalso configured to provide feedback from the control surfaces 403 andthe propulsion system 402 to the navigation system 15 and the CVG system100 during flight to provide for correction or adjustments to thecourse. In yet other aspects, the navigation system 15 and the CVGsystem 100 described herein is a part of the aerospace vehiclecontroller 401 (as shown in dashed lines) and is in direct communicationwith the propulsion system 402 and/or the control surfaces 403. In yetother aspects, the navigation system 15 and CVG system 100 is in directcommunication with the propulsion system and/or the control surfaces403. Any number of other systems may be included. The principles of theinvention may be applied to other industries, including, for example,personal electronics (global positioning system receivers orsmartphones).

In accordance with one or more aspects of the present disclosure thefollowing are provided:

A1. A method comprising:

supplying a first voltage input to a Coriolis vibratory gyroscope at afirst bias voltage;

supplying a second voltage input to the Coriolis vibratory gyroscope ata second bias voltage, the second bias voltage being different than thefirst bias voltage;

detecting a difference in responses of the Coriolis vibratory gyroscopeto the first bias voltage and the second bias voltage; and

determining a gyro rate of the Coriolis vibratory gyroscope as afunction of the difference in responses and a correction term.

A2. The method of claim A1, wherein the Coriolis vibratory gyroscopeoutputs a first response in response to the first bias voltage and asecond response in response to the second bias voltage and thecorrection term represents a sum of the time dependent instrument biasin the first response and the second response.

A3. The method of claim A1, wherein the gyro rate of the Coriolisvibratory gyroscope is determined independent of a scale factor of theCoriolis vibratory gyroscope.

A4. The method of claim A1, wherein the correction term is apredetermined constant value based on an initial voltage output andinitial input rate of the Coriolis vibratory gyroscope at the first biasvoltage and the second bias voltage.

A5. The method of claim A1, wherein a change in voltage output of theCoriolis vibratory gyroscope from a first response at the first biasvoltage to a second response at the second bias voltage provides a firstscale factor corresponding to the first response and a second scalefactor corresponding to the second response for a common voltage inputto the Coriolis vibratory gyroscope.

A6. The method of claim A5, wherein the gyro rate (Ω) is determined fromthe equation

$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$

where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage. V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.

A7. The method of claim A6, wherein the difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage is constant.

A8. The method of claim A5, further comprising continuing to determinethe gyro rate of the Coriolis vibratory gyroscope, as the function ofthe difference in responses and the correction term, independent ofcalibration of the first scale factor and calibration of the secondscale factor where the time dependent instrument bias causes the firstscale factor and the second scale factor to shift equally.

A9. The method of claim A1, further comprising navigating a vehicle froma first location to a second location with the Coriolis vibratorygyroscope.

B1. A navigation system comprising:

a Coriolis vibratory gyroscope;

a voltage input supply configured to

supply a first voltage input to the Coriolis vibratory gyroscope at afirst bias voltage, and

supply a second voltage input to the Coriolis vibratory gyroscope at asecond bias voltage, the second bias voltage being different than thefirst bias voltage; and

a controller configured to detect a difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage, and determine a gyro rate of the Coriolis vibratorygyroscope as a function of the difference in responses and a correctionterm.

B2. The navigation system of claim B1, wherein the Coriolis vibratorygyroscope outputs a first response in response to the first bias voltageand a second response in response to the second bias voltage and thecorrection term represents a sum of the time dependent instrument biasin the first response and the second response.

B3. The navigation system of claim B1, wherein the controller isconfigured to determine the gyro rate of the Coriolis vibratorygyroscope independent of a scale factor of the Coriolis vibratorygyroscope.

B4. The navigation system of claim B1, wherein the correction term is apredetermined constant value based on an initial voltage output andinitial input rate of the Coriolis vibratory gyroscope at the first biasvoltage and the second bias voltage.

B5. The navigation system of claim B1, wherein a change in voltageoutput of the Coriolis vibratory gyroscope from a first response at thefirst bias voltage to a second response at the second bias voltageprovides a first scale factor corresponding to the first response and asecond scale factor corresponding to the second response for a commonvoltage input to the Coriolis vibratory gyroscope.

B6. The navigation system of claim B5, wherein the gyro rate (Ω) isdetermined from the equation

$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$

where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage. V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.

B7. The navigation system of claim B6, wherein the difference inresponses of the Coriolis vibratory gyroscope to the first bias voltageand the second bias voltage is constant.

B8. The navigation system of claim B5, wherein the controller isconfigured to continue to determine the gyro rate of the Coriolisvibratory gyroscope, as the function of the difference in responses andthe correction term, independent of calibration of the first scalefactor and calibration of the second scale factor where the timedependent instrument bias causes the first scale factor and the secondscale factor to shift equally.

B9. The navigation of claim B1, wherein the controller is configured tonavigate a vehicle from a first location to a second location with theCoriolis vibratory gyroscope.

C1. A vehicle comprising:

a navigation system including

-   -   a Coriolis vibratory gyroscope;

a voltage input supply configured to

supply a first voltage input to the Coriolis vibratory gyroscope at afirst bias voltage, and

supply a second voltage input to the Coriolis vibratory gyroscope at asecond bias voltage, the second bias voltage being different than thefirst bias voltage;

a controller configured to detect a difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage, and determine a gyro rate of the Coriolis vibratorygyroscope as a function of the difference in responses and a correctionterm.

C2. The vehicle of claim C1, wherein the Coriolis vibratory gyroscopeoutputs a first response in response to the first bias voltage and asecond response in response to the second bias voltage and thecorrection term represents a sum of the time dependent instrument biasin the first response and the second response.

C3. The vehicle of claim C1, wherein the controller is configured todetermine the gyro rate of the Coriolis vibratory gyroscope independentof a scale factor of the Coriolis vibratory gyroscope.

C4. The vehicle of claim C1, wherein the correction term is apredetermined constant value based on an initial voltage output andinitial input rate of the Coriolis vibratory gyroscope at the first biasvoltage and the second bias voltage.

C5. The vehicle of claim C1, wherein a change in voltage output of theCoriolis vibratory gyroscope from a first response at the first biasvoltage to a second response at the second bias voltage provides a firstscale factor corresponding to the first response and a second scalefactor corresponding to the second response for a common voltage inputto the Coriolis vibratory gyroscope.

C6. The vehicle of claim C5, wherein the gyro rate (Ω) is determinedfrom the equation

$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$

where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.

C7. The vehicle of claim C6, wherein the difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage is constant.

C8. The vehicle of claim C5, wherein the controller is configured tocontinue to determine the gyro rate of the Coriolis vibratory gyroscope,as the function of the difference in responses and the correction term,independent of calibration of the first scale factor and calibration ofthe second scale factor where the time dependent instrument bias causesthe first scale factor and the second scale factor to shift equally.

C9. The vehicle of claim C1, wherein the controller is configured tonavigate the vehicle from a first location to a second location with theCoriolis vibratory gyroscope.

D1. A system comprising:

a Coriolis vibratory gyroscope;

a voltage input supply configured to

supply a first voltage input to the Coriolis vibratory gyroscope at afirst bias voltage, and

supply a second voltage input to the Coriolis vibratory gyroscope at asecond bias voltage, the second bias voltage being different than thefirst bias voltage; and

a controller configured to detect a difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage, and determine a gyro rate of the Coriolis vibratorygyroscope as a function of the difference in responses and a correctionterm.

D2. The system of claim D1, wherein the Coriolis vibratory gyroscopeoutputs a first response in response to the first bias voltage and asecond response in response to the second bias voltage and thecorrection term represents a sum of the time dependent instrument biasin the first response and the second response.

D3. The system of claim D1, wherein the controller is configured todetermine the gyro rate of the Coriolis vibratory gyroscope independentof a scale factor of the Coriolis vibratory gyroscope.

D4. The system of claim D1, wherein the correction term is apredetermined constant value based on an initial voltage output andinitial input rate of the Coriolis vibratory gyroscope at the first biasvoltage and the second bias voltage.

D5. The system of claim D1, wherein a change in voltage output of theCoriolis vibratory gyroscope from a first response at the first biasvoltage to a second response at the second bias voltage provides a firstscale factor corresponding to the first response and a second scalefactor corresponding to the second response for a common voltage inputto the Coriolis vibratory gyroscope.

D6. The system of claim D5, wherein the gyro rate (Ω) is determined fromthe equation

$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$

where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage. V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.

D7. The system of claim D6, wherein the difference in responses of theCoriolis vibratory gyroscope to the first bias voltage and the secondbias voltage is constant.

D8. The system of claim D5, wherein the controller is configured tocontinue to determine the gyro rate of the Coriolis vibratory gyroscope,as the function of the difference in responses and the correction term,independent of calibration of the first scale factor and calibration ofthe second scale factor where the time dependent instrument bias causesthe first scale factor and the second scale factor to shift equally.

D9. The system of claim D1, wherein the controller is configured tonavigate a vehicle from a first location to a second location with theCoriolis vibratory gyroscope.

E1. A method comprising:

determining scale factors for a first voltage input at a first biasvoltage and a second voltage input at a second bias voltage for aCoriolis vibratory gyroscope:

providing the first voltage input to the Coriolis vibratory gyroscope atthe first bias voltage and detecting a first response of the Coriolisvibratory gyroscope;

providing the second voltage input to the Coriolis vibratory gyroscopeat the second bias voltage and detecting a second response of theCoriolis vibratory gyroscope; and

using a difference of the first response and the second response, thescale factors for the first voltage input and the second voltage inputand a gyro rate of the Coriolis vibratory gyroscope to determine acorrection term representing a function of a difference of the timedependent instrument bias in the first response and the second response.

E2. The method of claim E5, wherein the correction term (C) isdetermined from the equation

$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$

where S₀ is a first scale factor corresponding to the first response andS₀′ is a second scale factor corresponding to the second response with(1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage. V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.

Different examples and aspects of the system and methods are disclosedherein that include a variety of components, features, andfunctionality. It should be understood that the various examples andaspects of the system and methods disclosed herein may include any ofthe components, features, and functionality of any of the other examplesand aspects of the system and methods disclosed herein in anycombination, and all of such possibilities are intended to be within thespirit and scope of the present disclosure.

Many modifications and other examples of the disclosure set forth hereinwill come to mind to one skilled in the art to which the disclosurepertains having the benefit of the teachings presented in the foregoingdescriptions and the associated drawings.

Therefore, it is to be understood that the disclosure is not to belimited to the specific embodiments disclosed and that modifications andother embodiments are intended to be included within the scope of theappended claims. Moreover, although the foregoing descriptions and theassociated drawings describe example embodiments in the context ofcertain illustrative combinations of elements and/or functions, itshould be appreciated that different combinations of elements and/orfunctions may be provided by alternative implementations withoutdeparting from the scope of the appended claims.

What is claimed is:
 1. A method comprising: supplying a first voltageinput to a Coriolis vibratory gyroscope at a first bias voltage;supplying a second voltage input to the Coriolis vibratory gyroscope ata second bias voltage, the second bias voltage being different than thefirst bias voltage; detecting a difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage; and determining a gyro rate of the Coriolis vibratory gyroscopeas a function of the difference in responses and a correction term. 2.The method of claim 1, wherein the Coriolis vibratory gyroscope outputsa first response in response to the first bias voltage and a secondresponse in response to the second bias voltage and the correction termrepresents a sum of the time-dependent instrument bias in the firstresponse and the second response.
 3. The method of claim 1, wherein thegyro rate of the Coriolis vibratory gyroscope is determined independentof a scale factor of the Coriolis vibratory gyroscope.
 4. The method ofclaim 1, wherein the correction term is a predetermined constant valuebased on an initial voltage output and initial input rate of theCoriolis vibratory gyroscope at the first bias voltage and the secondbias voltage.
 5. The method of claim 1, wherein a change in voltageoutput of the Coriolis vibratory gyroscope from a first response at thefirst bias voltage to a second response at the second bias voltageprovides a first scale factor corresponding to the first response and asecond scale factor corresponding to the second response for a commonvoltage input to the Coriolis vibratory gyroscope.
 6. The method ofclaim 5, wherein the gyro rate (Ω) is determined from the equation$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.
 7. The method of claim 6, wherein the difference in responses ofthe Coriolis vibratory gyroscope to the first bias voltage and thesecond bias voltage is constant.
 8. The method of claim 5, furthercomprising continuing to determine the gyro rate of the Coriolisvibratory gyroscope, as the function of the difference in responses andthe correction term, independent of calibration of the first scalefactor and calibration of the second scale factor where the timedependent instrument bias causes the first scale factor and the secondscale factor to shift equally.
 9. The method of claim 1, furthercomprising navigating a vehicle from a first location to a secondlocation with the Coriolis vibratory gyroscope.
 10. A system comprising:a Coriolis vibratory gyroscope; a voltage input supply configured tosupply a first voltage input to the Coriolis vibratory gyroscope at afirst bias voltage, and supply a second voltage input to the Coriolisvibratory gyroscope at a second bias voltage, the second bias voltagebeing different than the first bias voltage; and a controller configuredto detect a difference in responses of the Coriolis vibratory gyroscopeto the first bias voltage and the second bias voltage, and determine agyro rate of the Coriolis vibratory gyroscope as a function of thedifference in responses and a correction term.
 11. The system of claim10, wherein the Coriolis vibratory gyroscope outputs a first response inresponse to the first bias voltage and a second response in response tothe second bias voltage and the correction term represents a sum of thetime dependent instrument bias in the first response and the secondresponse.
 12. The system of claim 10, wherein the controller isconfigured to determine the gyro rate of the Coriolis vibratorygyroscope independent of a scale factor of the Coriolis vibratorygyroscope.
 13. The system of claim 10, wherein the correction term is apredetermined constant value based on an initial voltage output andinitial input rate of the Coriolis vibratory gyroscope at the first biasvoltage and the second bias voltage.
 14. The system of claim 10, whereina change in voltage output of the Coriolis vibratory gyroscope from afirst response at the first bias voltage to a second response at thesecond bias voltage provides a first scale factor corresponding to thefirst response and a second scale factor corresponding to the secondresponse for a common voltage input to the Coriolis vibratory gyroscope.15. The system of claim 14, wherein the gyro rate (Ω) is determined fromthe equation$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$where S₀ is the first scale factor and S₀′ is the second scale factorwith (1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.
 16. The system of claim 15, wherein the difference in responses ofthe Coriolis vibratory gyroscope to the first bias voltage and thesecond bias voltage is constant.
 17. The system of claim 14, wherein thecontroller is configured to continue to determine the gyro rate of theCoriolis vibratory gyroscope, as the function of the difference inresponses and the correction term, independent of calibration of thefirst scale factor and calibration of the second scale factor where thetime dependent instrument bias causes the first scale factor and thesecond scale factor to shift equally.
 18. The system of claim 10,wherein the controller is configured to navigate a vehicle from a firstlocation to a second location with the Coriolis vibratory gyroscope. 19.A method comprising: determining scale factors for a first voltage inputat a first bias voltage and a second voltage input at a second biasvoltage for a Coriolis vibratory gyroscope; providing the first voltageinput to the Coriolis vibratory gyroscope at the first bias voltage anddetecting a first response of the Coriolis vibratory gyroscope;providing the second voltage input to the Coriolis vibratory gyroscopeat the second bias voltage and detecting a second response of theCoriolis vibratory gyroscope; and using a difference of the firstresponse and the second response, the scale factors for the firstvoltage input and the second voltage input and a gyro rate of theCoriolis vibratory gyroscope to determine a correction term representinga function of a difference of the time dependent instrument bias in thefirst response and the second response.
 20. The method of claim 19,wherein the correction term (C) is determined from the equation$\Omega = \frac{\left( {V_{0} - V_{0}^{\prime} - C} \right)}{\frac{1}{S_{0}} - \frac{1}{S_{0}^{\prime}}}$where S₀ is a first scale factor corresponding to the first response andS₀′ is a second scale factor corresponding to the second response with(1/S₀)−(1/S₀′) being the difference in responses of the Coriolisvibratory gyroscope to the first bias voltage and the second biasvoltage, V₀ is the first response at the first bias voltage, V₀′ is thesecond response at the second bias voltage, and C is the correctionterm.